A "bog standard" Engine Failure, where you are going to drone through 20 minutes of QRH/ECAM drills, DODAR, and only then decide where you are going to divert to, seems a Pan to me - no immediate assistance required.
Forgive me my ignorance, but I'm just a simple-minded ATR F/O, who usually goes through engine fire or engine flameout checklist items in less than a minute (in a simulator anyway), then switches to single engine operation checklist, and that one begins with:
LAND ASAP
I really had no idea that you oh-so-big boys flying oh-so-big jets need 20 mins to do your ECAM drills and only then decision making kicks in. I need to learn a lot more before I get upgraded. Hey, is this the way BA EFATO turned into transatlantic flight? Perhaps by the time the crew completed QRH drill, plane has owerflown the middle of Atlantic?
If the guy has food poisoning, but you are continuing
If the guy survives food poisoning, recovers and finds out that his other CM proceedeed to destination (if there was alternate available) because s/he was unable to properly plan and execute diversion on her/his own, the said guy might find it very hard to supress natural instinct towards decapitation of that other CM.
Once again: type and amount of airport emergency services that greet you on your arrival have nothing to do with pan or mayday, it's something you have requested or something that your ATCO has requested. And here comes the anectode: DHC-7 inbound south German airfield suffers engine failure. It's reported to ATC, but as destination is near, there's no pan or mayday and crew proceeds to destination. On final they notice a lot of ambulances waiting around the runway. Capt comments to F/O:"There's probably some bigger plane in trouble behind us, let's vacate as quick as we can". Landing goes uneventful and upon vacating capt asks ATC who are the ambulances waiting for. Answer: "You". Next question, coming in a bit puzzled tone, was: "Why so many?". ATCO replies: "Because each of your passengers might need an ambulance". While capt initially thought of it as overreaction, later he admitted that ATCO had a good point.
Moral of the story: if you need to have emergency, have it over Germany.